Question 1194135
the answer from chegg is not correct.
the formula that i came up with is y = 20 * cos(28.8 * (x-3)) + 32.
the graph of that formula is shown below.
<img src = "http://theo.x10hosting.com/2022/051004.jpg">
you have low tide of 12 inches at x = 9.25 and high tide of 52 inches at x = 15.5
x = 9.25 is equal to 9 hours and 15 minutes from midnight which makes it equal to 9:30 am on a 12 hour clock and 0930 on a 24 hour clock.
x = 15.5 is equal to 15 hours and 30 minutes from midnight which makes it equal to 1530 on a 24 hour clock which makes it equal to 3:30 pm on a 12 hour clock.
let me know if you have any questions.
theo


addition information to answer your questions are below.


i wanted the period to be 6.25 hours.
since this was half the cycle of the cosine function, i used the formula of frequency = 180 / 6.25 rather than frequency = 360/6.25
180/6.25 gave me a frequency of 28.8 which is what i used.


the shift of 3 units was because the cosine function, without a shift, gave me a value of y = 12 when x was 6.25.
i wanted a value of 12 when x was 9.25.
the difference was 3 units of x.
that's what i used (x-3) rather than x.


here is the graph of both functions so you can see why the shift was 3 units.


<img src = "http://theo.x10hosting.com/2022/051301.jpg" >


i did use the graphing software to guide me.
without that, it may not have been that straight forward.
my answer is not the standard answer, but i thought it made sense and so i gave it to you.


let me know if you have any further questions.
theo